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Mathematics - Application of Derivative Question with Solution | TestHub

MathematicsApplication of DerivativeMaxima-MinimaHard2 minQB

MathematicsHardsingle choice

Let $f (x) = sin^{3} x + λ sin^{2} x$ on $(- π /2, π /2)$ . How many integral values of $λ$ make $f$ have exactly one minimum and one maximum?

Options:

Answer:

Solution:

$f_{'} = sin x cos x (3 sin x + 2 λ)$ . Besides $x = 0$ , exactly one further interior stationary point exists when $0 < ∣ λ ∣ < 3/2$ . The integral values are $λ = \pm 1$ , giving two values.

Stream:JEESubject:MathematicsTopic:Application of DerivativeSubtopic:Maxima-Minima

⏱ 2mℹ️ Source: QB

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